1. Field of the Invention
The present invention relates to an optical device used for optical communication. In particular, the present invention relates to an optical device such as an optical separator, an optical filter, a light transmitting/receiving module for WDM (wavelength division multiplexing), an optical inductor, a bend waveguide, and an optical deflector.
2. Description of the Related Art
FIG. 17 shows an example of an optical separator utilizing a Y-separation waveguide, which is a conventional optical device. Light is incident upon a Y-separator 184 having an optical waveguide structure through an ingoing optical fiber 181. Light propagating through a Y-shaped core 186 is separated to outgoing optical fibers 182 and 183. The Y-separator 184 has a configuration in which a Y-shaped core 186 is formed on a substrate 185.
In a conventional optical device, in order to couple light in the ingoing optical fiber 181, the Y-separator 184 with an optical waveguide structure and the outgoing optical fibers 182 and 183, it is necessary to conduct the alignment of optical axes and matching in mode shapes with high precision, which requires a high skill for assembling such an optical separator. In addition, since a separation angle of the Y-separator 184 is at most about 4xc2x0, when the length of the Y-separator 184 is set to be too small, there is insufficient light separation, which makes it difficult to miniaturize the optical separator.
A conventional transmitting/receiving module for WDM will be described with reference to FIG. 18. The transmitting/receiving module for WDM is composed of an optical waveguide and a multi-layer filter.
On a substrate 191, an optical waveguide 197, a photodiode (1.3 xcexcm) 193, a laser diode (1.55 xcexcm) 194, a photodiode (1.55 xcexcm) 195, and a optical fiber 192 are placed.
The optical waveguide 197 is provided with a cladding 197d, a first core 197a, a second core 197b, a third core 197c, and a WDM dielectric multilayer filter (1.3/1.55 xcexcm) 198. The first core 197a, the second core 197b, and the third core 197c constitute a Y-shaped core, and the WDM dielectric multi-layer filter (1.3/1.55 xcexcm) 198 is formed so as to divide these cores.
The photodiode (1.3 xcexcm) 193 is disposed on the substrate 191 so as to be coupled to the first core 197a. Furthermore, the optical fiber 192 is fixed in a V-groove 196 formed on the substrate 191 so as to be coupled to the second core 197b. Furthermore, the laser diode (1.55 xcexcm) 194 and the photodiode (1.55 xcexcm) 195 are disposed on the substrate 191 so as to be coupled to the third core 197c. 
When signal light of 1.3/1.55 xcexcm WDM is incident upon the second core 197b from the optical fiber 192, the signal light is separated by the multi-layer filter 198. Then, light (1.3 xcexcm) propagates to the first core 197a, and light (1.55 xcexcm) propagates to the third core 197c. The light propagating to the first core 197a is received by the photodiode (1.3 xcexcm) 193. Similarly, the light propagating to the third core 197c is received by the photodiode (1.55 xcexcm) 195. Furthermore, signal light emitted from the laser diode (1.55 xcexcm) 194 propagates to the third core 197c. Then, the signal light is guided to the second core 197b by the multi-layer filter 198 and sent to the optical fiber 192. An arrow 199a represents a propagation direction of the light (1.3 xcexcm), and an arrow 199b represents a propagation direction of the light (1.55 xcexcm).
As described above, by using the WDM transmitting/receiving module, bidirectional communication can be conducted with light (1.55 xcexcm), and communication of receiving only can be conducted with light (1.3 xcexcm).
However, the conventional WDM transmitting/receiving module requires the optical waveguide 197 having a Y-shaped core and the multi-layer filter 198 for separation of a wavelength. This increases the number of components, making it difficult to achieve a low cost.
In order to solve the above-mentioned problem, constituting an optical device such as an optical separator and an optical filter with a photonic crystal has drawn attention. For example, JP11(1999)-271541 discloses a wavelength separating filter using a photonic crystal with a two-dimensional triangular lattice.
In the present specification, the term xe2x80x9cphotonic crystalxe2x80x9d refers to an artificial multi-dimensional periodic structure substantially having a period of a light wavelength.
FIGS. 19A and 19B show a configuration of the wavelength separating filter using a photonic crystal disclosed by JP11(1999)-271541. In this configuration, materials with different refractive indexes are arranged periodically, whereby strong deflection dispersion characteristics (which are not found in general optical crystal) are obtained to control wavelength deflection. Specifically, as shown in FIG. 19A, the wavelength separating filter has a configuration in which a substrate 200, which has atomic media 204 embedded in a background medium 203 in a two-dimensional triangular arrangement, is interposed between a first cladding 201 and a second cladding 202. As shown in FIG. 19B, an incident surface 208 of a light signal is tilted at a predetermined angle with respect to an incident direction 207 of the light signal, and the light signal is output from an output surface 209. The interval between the adjacent atomic media 204 is designed in accordance with the wavelength of a light signal. The thickness of the substrate 200 is designed in such a manner that a light signal is confined sufficiently in the substrate 200, and a light traveling direction does not deviate largely from the surface of the substrate 200.
The above-mentioned photonic crystal with a two-dimensional triangular lattice has a structure in which lattice vectors are matched with reciprocal lattice vectors. Even if light is incident upon a photonic crystal with such a structure in a lattice vector direction, strong deflection dispersion characteristics cannot be obtained. In order to obtain strong deflection dispersion characteristics, it is required to set a light incident surface of the photonic crystal so as to be non-vertical to a lattice vector direction or to tilt the light incident surface with respect to an incident surface vertical to the lattice vector direction, thereby allowing light to be incident upon the photonic crystal. Therefore, the incident surface 208 is tilted at a predetermined angle with respect to the incident direction 207 of a light signal in FIG. 19B.
Next, a relationship between primitive lattice vectors (a1, a2) and basic reciprocal lattice vectors (b1, b2) will be described. FIGS. 20A to 20C respectively show a relationship between a lattice and a Brillouin zone. FIG. 20A shows a tetragonal lattice, and FIG. 20B shows a triangular lattice. In each of FIGS. 20A to 20C, the upper stage shows a lattice space, whereas the lower stage shows a reciprocal lattice space. Reference numeral 211 denotes atomic media constituting a lattice, and 212 denotes a Brillouin zone. The tetragonal lattice and the triangular lattice respectively have a symmetric structure (for example, an interior angle equal to or smaller than 90xc2x0 between the primitive lattice vectors is 45xc2x0, 60xc2x0, 90xc2x0, or the like). Important symmetric points of the Brillouin zone 212 in the tetragonal lattice and the triangular lattice shown in FIGS. 20A and 20B are two points (X, M) and (M, K), respectively. With such a structure, incident light to the primitive lattice vectors (a1, a2) does not exhibit deflection characteristics because the direction of the incident light is matched with the direction of the important symmetric point of the Brillouin zone 212.
On the other hand, in the case of an oblique lattice with low symmetry as shown in FIG. 20C, for example, when an interior angle xcex8 between the primitive lattice vectors (a1, a2) is larger than 60xc2x0 and smaller than 90xc2x0, the important symmetric points of the Brillouin zone become three points (H1, H2, H3). In this case, the direction of the incident light in the primitive lattice vectors (a1, a2) is not matched with the direction of important points of the Brillouin zone, so that deflection dispersion is exhibited. Therefore, even if light is allowed to be incident vertically upon an incident surface vertical to the primitive lattice vectors (a1, a2), strong deflection dispersion characteristics are exhibited.
JP11(1999)-271541 describes lattice arrangements such as a tetragonal lattice, in addition to the triangular lattice. In the case of the other lattice arrangements, an optical system is varied in a complicated manner due to the relationship between the Brillouin zone and the lattice vectors. Accordingly, in the lattice arrangements other than those with high symmetry such as a tetragonal lattice, useful deflection dispersion characteristics cannot be obtained in an optical system similar to that of a triangular lattice.
That is, in the case of forming the optical separator 184 shown in FIG. 17, and the multi-layer filter 198 constituting the WDM transmitting/receiving module shown in FIG. 18, using a photonic crystal with high symmetry, it is required to set an incident surface of the photonic crystal so as to be non-vertical to the primitive lattice vectors (a1, a2), or to tilt the incident surface with respect to an incident surface vertical to the primitive lattice vectors (a1, a2).
Therefore, not only treatment precision for producing a photonic crystal, but also higher incident angle precision of an optical system are required. This makes it difficult for an optical device to be formed of a photonic crystal with high symmetry.
Therefore, with the foregoing in mind, it is an object of the present invention to provide an optical device that can be miniaturized using a simple optical system with a small number of components without requiring a complicated optical system, a high-degree Y-shaped waveguide, and a multilayer filter.
In order to achieve the above-mentioned object, an optical device of the present invention includes a photonic crystal having a two-dimensional or three-dimensional lattice structure in which a plurality of materials with different refractive indexes are arranged periodically, wherein a two-dimensional lattice structure composed of a group of primitive lattice vectors has a lattice structure having no rotation axis of more than 3-fold. Because of this, an optical device having strong deflection dispersion characteristics can be realized.
The above-mentioned optical device may include an incident portion for allowing light to be incident in a direction of the primitive lattice vector of the photonic crystal.
Furthermore, the photonic crystal may have an incident surface vertical to the direction of the primitive lattice vector, and the incident portion may be disposed so as to allow light to be incident vertically to the incident surface.
Furthermore, in the photonic crystal, an angle equal to or smaller than 90xc2x0 between at least two different primitive lattice vectors among a plurality of primitive lattice vectors may be larger than 60xc2x0 and smaller than 90xc2x0.
Another optical device of the present invention includes a photonic crystal containing a first material and a plurality of columnar materials, wherein the plurality of columnar materials have a refractive index different from a refractive index of the first material and are disposed in the first material, and central axes of the plurality of columnar materials are parallel to each other, whereby a two-dimensional crystal lattice arrangement having a constant periodicity is formed, and a two-dimensional lattice structure composed of a group of primitive lattice vectors has a lattice structure having no rotation axis of more than 3-fold. According to this configuration, since a photonic crystal with low symmetry is used, an optical device having strong deflection dispersion characteristics can be realized.
Furthermore, another optical device of the present invention includes a photonic crystal containing a first material and a plurality of columnar materials, wherein the plurality of columnar materials have a refractive index different from a refractive index of the first material and are disposed in the first material, and central axes of the plurality of columnar materials are parallel to each other, whereby a two-dimensional crystal lattice arrangement having a constant periodicity is formed, and an angle equal to or smaller than 90xc2x0 between two primitive lattice vectors is larger than 60xc2x0 and smaller than 90xc2x0. Because of this, a plurality of columnar materials can be arranged periodically without interference, so that an optical device having strong deflection dispersion characteristics can be realized.
Furthermore, it is preferable that the photonic crystal is in a slab shape, the optical device further comprises a first cladding and a second cladding that have a refractive index lower than the refractive index of the first material of the photonic crystal, and the first cladding and the second cladding are disposed so as to be in contact with either side of the photonic crystal in the slab shape in a thickness direction. Because of this, an optical device can be realized in which light propagating through the photonic crystal does not leak.
Furthermore, it is preferable that the above-mentioned optical device includes an incident portion for allowing light to be incident in a direction of the primitive lattice vector of the photonic crystal. Because of this, an optical device can be formed easily in which light with a predetermined wavelength can be deflected at a large angle.
Furthermore, the photonic crystal may have an incident surface vertical to the direction of the primitive lattice vector, and the incident portion may be disposed so as to allow light to be incident vertically to the incident surface.
Furthermore, it is preferable that a lattice constant of a two-dimensional lattice of the photonic crystal is 0.4 to 0.6 times a wavelength of a light source to be used. Because of this, high deflection dispersion characteristics can be obtained.
Furthermore, each of the columnar materials may have a cylindrical shape, and a radius thereof may be 0.2 to 0.5 times a lattice constant.
Furthermore, a refractive index of the first material may be 1.4 to 1.6, and a refractive index of the columnar materials may be 0.9 to 1.1.
Furthermore, a difference between a refractive index of the first material and a refractive index of the columnar materials may be at least 1.0.
Furthermore, the first material may be made of a resin material, and the columnar materials may be made of air.
Furthermore, it is preferable that the above-mentioned optical device includes an ingoing optical waveguide for allowing light to be incident in a direction of a primitive lattice vector of the photonic crystal, and a first outgoing optical waveguide and a second outgoing optical waveguide for receiving an output from the photonic crystal. Because of this, a miniaturized optical filter can be formed easily at a low cost, in which light with a desired wavelength can be separated from a plurality of light beams.
Furthermore, it is preferable that the above-mentioned optical device includes: an ingoing optical fiber for allowing light to be incident in a direction of a primitive lattice vector of the photonic crystal; a first outgoing optical fiber and a second outgoing optical fiber for receiving an output from the photonic crystal; and grooves for positioning the ingoing optical fiber, the first outgoing optical fiber, and the second outgoing optical fiber. Because of this, an optical filter capable of easily conducting alignment of optical axes and matching in mode shapes can be realized even using an optical fiber.
Furthermore, an optical axis of the first outgoing optical fiber substantially may be matched with an optical axis of the ingoing optical fiber, and an optical axis of the second outgoing optical fiber may be different from an optical axis of the ingoing optical fiber.
Furthermore, a distance between the optical axis of the second outgoing optical fiber and the optical axis of the ingoing optical fiber is proportional to a length of the photonic crystal in a direction of a primitive lattice vector.
Furthermore, the above-mentioned optical device may include a substrate having the grooves, wherein the substrate is integrated with the photonic crystal.
Furthermore, the grooves may be provided in the first cladding or the second cladding.
Furthermore, it is preferable that the above-mentioned optical device includes: an optical fiber allowing light with a first wavelength and light with a second wavelength to propagate; a first light-receiving portion for receiving the light with the first wavelength; a light-emitting portion for emitting the light with the first wavelength; a second light-receiving portion for receiving the light with the second wavelength; and a substrate for fixing the optical fiber, the first light-receiving portion, the light-emitting portion, and the second light-receiving portion on a flat surface, wherein the optical fiber is disposed at one end of the photonic crystal, and an optical axis of the optical fiber is in parallel with a direction of a primitive lattice vector of the photonic crystal, the first light-receiving portion and the light-emitting portion are disposed in the same straight line as that of an optical axis of the optical fiber at the other end of the photonic crystal, and the second light-receiving portion is disposed at the other end of the photonic crystal. Because of this, a miniaturized WDM transmitting/receiving module can be realized easily at a low cost.
Furthermore, it is preferable that a lattice constant of a two-dimensional lattice of the photonic crystal is 0.4 to 0.6 times the second wavelength. Because of this, high deflection dispersion characteristics can be obtained.
Furthermore, each of the columnar materials may have a cylindrical shape, and a radius thereof may be 0.2 to 0.5 times a lattice constant.
Furthermore, a refractive index of the first material may be 1.4 to 1.6, and a refractive index of the columnar materials may be 0.9 to 1.1.
Furthermore, a difference between a refractive index of the first material and a refractive index of the columnar materials may be at least 1.0.
Furthermore, the first material may be made of a resin material, and the columnar materials may be made of air.
Furthermore, the above-mentioned optical device may include: an optical fiber allowing light with a first wavelength and light with a second wavelength to propagate; a first light-receiving portion for receiving the light with the first wavelength; a light-emitting portion for emitting the light with the second wavelength; a second light-receiving portion for receiving the light with the second wavelength; and a substrate for fixing the optical fiber, the first light-receiving portion, the light-emitting portion, and the second light-receiving portion on a flat surface, wherein the optical fiber is disposed at one end of the photonic crystal, and an optical axis of the optical fiber is in parallel with a direction of a primitive lattice vector of the photonic crystal, the first light-receiving portion is disposed in the same straight line as that of an optical axis of the optical fiber at the other end of the photonic crystal, and the second light-receiving portion and the light-emitting portion are disposed at the other end of the photonic crystal.
Furthermore, it is preferable that a lattice constant of a two-dimensional lattice of the photonic crystal is 0.4 to 0.6 times the second wavelength. Because of this, high deflection dispersion characteristics can be obtained.
Furthermore, each of the columnar materials may have a cylindrical shape, and a radius thereof may be 0.2 to 0.5 times a lattice constant.
Furthermore, a refractive index of the first material may be 1.4 to 1.6, and a refractive index of the columnar materials may be 0.9 to 1.1.
Furthermore, a difference between a refractive index of the first material and a refractive index of the columnar materials may be at least 1.0.
Furthermore, the first material may be made of a resin material, and the columnar materials may be made of air.
Furthermore, another optical device of the present invention includes a composite photonic crystal in which two kinds of photonic crystals are bonded to each other so that respective primitive lattice vectors are aligned in the same direction, wherein each of the photonic crystals contains a first material and a plurality of columnar materials, the plurality of columnar materials have a refractive index different from a refractive index of the first material and are disposed in the first material, central axes of the plurality of columnar materials are parallel to each other, whereby a two-dimensional crystal lattice arrangement having a predetermined periodicity is formed, and an angle equal to or smaller than 90xc2x0 between the two primitive lattice vectors is larger than 60xc2x0 and smaller than 90xc2x0. Because of this, a miniaturized optical separator can be realized at a low cost.
Furthermore, it is preferable that the composite photonic crystal is in a slab shape, the optical device further comprises a first cladding and a second cladding that have a refractive index lower than the refractive index of the first material of the two kinds of photonic crystals of the composite photonic crystal, and the first cladding and the second cladding are disposed so as to be in contact with either side of the composite photonic crystal in a thickness direction. Because of this, an optical device can be realized in which light propagating through the photonic crystal does not leak.
Furthermore, primitive lattice vectors that are not in the same direction among primitive lattice vectors of the two kinds of photonic crystals may be axisymmetric with respect to a bonding surface between the two kinds of photonic crystals.
Furthermore, it is preferable that lattice constants of both two-dimensional lattices of the two kinds of photonic crystals are 0.4 to 0.6 times a wavelength of a light source to be used. Because of this, high deflection dispersion characteristics can be obtained.
Furthermore, each of the columnar materials may have a cylindrical shape, and a radius thereof may be 0.2 to 0.5 times a lattice constant.
Furthermore, a refractive index of the first material may be 1.4 to 1.6, and a refractive index of the columnar materials may be 0.9 to 1.1.
Furthermore, a difference between a refractive index of the first material and a refractive index of the columnar materials may be at least 1.0.
Furthermore, the first material may be made of a resin material, and the columnar materials may be made of air.
Furthermore, the above-mentioned optical device may include: an ingoing optical waveguide for allowing light to be incident upon a bonding portion of the composite photonic crystal in a direction of a primitive lattice vector of the two kinds of photonic crystals; a first outgoing optical waveguide for receiving an output from one photonic crystal of the composite photonic crystal; and a second outgoing optical waveguide for receiving an output from the other photonic crystal of the composite photonic crystal, wherein the ingoing optical waveguide is disposed at one end of the composite photonic crystal, and the first outgoing optical waveguide and the second outgoing optical waveguide are disposed at the other end of the composite photonic crystal.
It is preferable that the above-mentioned optical device includes: an ingoing optical fiber for allowing light to be incident upon a bonding portion of the composite photonic crystal in a direction of a primitive lattice vector of the two kinds of photonic crystals; a first outgoing optical fiber for receiving an output from one photonic crystal of the composite photonic crystal; a second outgoing optical fiber for receiving an output from the other photonic crystal of the composite photonic crystal; and grooves for positioning the ingoing optical fiber, the first outgoing optical fiber, and the second outgoing optical fiber, wherein the ingoing optical fiber is disposed at one end of the composite photonic crystal, and the first outgoing optical fiber and the second outgoing optical fiber are disposed at the other end of the composite photonic crystal. Because of this, an optical separator capable of easily conducting alignment of optical axes and matching in mode shapes can be realized even using an optical fiber.
Furthermore, the above-mentioned optical device may include a substrate having grooves, wherein the substrate is integrated with the composite photonic crystal.
Furthermore, the grooves may be provided in the first cladding or the second cladding.
Furthermore, it is preferable that parallel composite photonic crystals including a plurality of the composite photonic crystals in parallel with each other are disposed in tandem in multiple stages. Because of this, a separator capable of separating light into a plurality of beams as well as two beams can be formed.
Furthermore, another optical device of the present invention includes: a plurality of photonic crystals each containing a first material and a plurality of columnar materials, in which the plurality of columnar materials have a refractive index different from a refractive index of the first material and are disposed in the first material, central axes of the plurality of columnar materials are parallel to each other, whereby a two-dimensional crystal lattice arrangement having a predetermined periodicity is formed, and an angle equal to or smaller than 90xc2x0 between the two primitive lattice vectors is larger than 60xc2x0 and smaller than 90xc2x0; an ingoing optical waveguide and an outgoing optical waveguide; and a substrate on which the plurality of photonic crystals, the ingoing optical waveguide, and the outgoing optical waveguide are disposed. The plurality of photonic crystals are bonded in tandem in a direction of a primitive vector, each of the photonic crystals is disposed so that output light deflected by an adjacent photonic crystal is in the direction of the primitive lattice vector, and the ingoing optical waveguide and the outgoing optical waveguide are bonded to each of the photonic crystals positioned at both ends. Because of this, an optical deflector that changes a traveling direction of incident light and outputs it can be formed easily.
Furthermore, it is preferable that a lattice constant of a two-dimensional lattice of the plurality of photonic crystals may be 0.4 to 0.6 times a wavelength of a light source to be used. Because of this, high deflection dispersion characteristics can be obtained.
Furthermore, each of the columnar materials may have a cylindrical shape, and a radius thereof may be 0.2 to 0.5 times a lattice constant.
Furthermore, a refractive index of the first material may be 1.4 to 1.6, and a refractive index of the columnar materials may be 0.9 to 1.1.
Furthermore, a difference between a refractive index of the first material and a refractive index of the columnar materials may be at least 1.0.
Furthermore, the first material may be made of a resin material, and the columnar materials may be made of air.
Furthermore, a size, a shape, and a position of the plurality of photonic crystals may be determined so that a propagation distance of light in each of the plurality of photonic crystals becomes equal to each other.
Furthermore, an angle formed by incident light from the ingoing optical waveguide and output light from the outgoing optical waveguide may be equal to a sum of angles at which light is deflected in the plurality of photonic crystals.
Furthermore, another optical device of the present invention includes a photonic crystal obtained by pressing a slab-shaped first material formed on a substrate with a die having columnar projections whose central axes are parallel to each other and which have a constant periodicity, in a thickness direction of the first material, and removing the die from the slab-shaped material to open columnar holes in the first material. Because of this, the photonic crystal can be formed easily.
Furthermore, the first material may be formed by coating the substrate with a material having flowability, uniformly dispersing the material to adjust a thickness thereof, and curing the material.
Furthermore, it is preferable that the columnar holes provided in the first material are filled with another material having a refractive index different from that of the first material. Because of this, the characteristics of the photonic crystal can be changed easily.
Furthermore, another optical device of the present invention includes a photonic crystal obtained by forming a mask with a predetermined periodicity on a slab-shaped first material formed on a substrate, and etching an exposed portion of the mask to open columnar holes in the first material. Because of this, the photonic crystal can be formed easily.
Furthermore, the first material may be formed by coating the substrate with a material having flowability, uniformly dispersing the material to adjust a thickness thereof, and curing the material.
Furthermore, it is preferable that the columnar holes provided in the first material are filled with another material having a refractive index different from that of the first material. Because of this, the characteristics of the photonic crystal can be changed easily.
Furthermore, another optical device of the present invention includes a photonic crystal obtained by forming a mask with a predetermined periodicity on a slab-shaped first material formed on a substrate, irradiating the first material with an ion beam to form track portions in exposed portions of the mask, and corroding the track portions by soaking the first material in an alkali solution, thereby opening columnar holes in the first material. Because of this, the photonic crystal can be formed easily.
Furthermore, the first material may be formed by coating the substrate with a material having flowability, uniformly dispersing the material to adjust a thickness thereof, and curing the material.
Furthermore, it is preferable that the columnar holes provided in the first material are filled with another material having a refractive index different from that of the first material. Because of this, the characteristics of the photonic crystal can be changed easily.
Furthermore, another optical device of the present invention includes a photonic crystal obtained by forming convex portions with a predetermined periodicity on a substrate, coating regions between the convex portions with a material having flowability, dispersing the material on the substrate to adjust a thickness of the material, curing the material, removing the convex portions to open columnar holes, and filling the columnar holes with another material having a refractive index different from that of the material having flowability. Because of this, the photonic crystal can be formed easily.
Furthermore, another optical device of the present invention having a horizontal surface vertical to a stack direction, includes a substrate in which a predetermined periodic pattern is formed in a one-dimensional or two-dimensional structure in a horizontal direction on a stack surface tilted from the horizontal surface, and a photonic crystal having a two-dimensional periodic stack structure in which at least two kinds of materials with different refractive indexes are stacked alternately on the substrate. Because of this, the photonic crystal can be formed easily.
Furthermore, it is preferable that a periodicity of the predetermined periodic pattern is 0.4 to 0.6 times a wavelength of a light source to be used. Because of this, a photonic crystal having large deflection dispersion characteristics can be formed.
Furthermore, it is preferable that a tilt of the stack surface with respect to the horizontal surface is 5xc2x0 to 25xc2x0. Because of this, a photonic crystal with low symmetry can be formed easily.
Furthermore, another optical device of the present invention includes a substrate on which a predetermined periodic pattern is formed in a one-dimensional or two-dimensional structure so that an angle equal to or smaller than 90xc2x0 between two primitive lattice vectors of a two-dimensional lattice is larger than 60xc2x0 and smaller than 90xc2x0, and a photonic crystal having a two-dimensional or three-dimensional periodic stack structure in which at least two kinds of materials having different refractive indexes are stacked alternately on the substrate. Because of this, a photonic crystal with low symmetry can be formed easily.
Furthermore, it is preferable that a periodicity of the predetermined periodic pattern is 0.4 to 0.6 times a wavelength of a light source to be used. Because of this, a photonic crystal having large deflection dispersion characteristics can be formed.
These and other advantages of the present invention will become apparent to those skilled in the art upon reading and understanding the following detailed description with reference to the accompanying figures.